Question

Question: To suck lemonade of density 1000 kg / $m^3$up a straw to a maximum height of 4.0 cm , what minimum gauge pressure (in atmospheres) must you produce in your lungs?

Short answer

Answer:

Gauge pressure produced in the lungs in atmospheric unit is$-3.9\times {10}^{-3}$atm

Step-by-step solution

The given data 

Maximum height,$h=4cmor0.04m$

Density of lemonade, $\rho =1000kg/m^3$

Acceleration due to gravity,$g=9.8m/s^2$$g=9.8m/s^2$

Understanding the concept of pressure 

To find gauge pressure in theatm, we can use the formula for pressure in terms of density, acceleration due to gravity, and height. Using the conversion factor, we can convert the pressure into atmospheric pressure.

Formula:

Pressure applied on a body, $p=\rho gh$ (i)

Calculation of gauge pressure in atm 

The pressure produced in the lungs in SI unit using equation (i) can be given as follows:

$$\begin{gathered} p=1000kg/m^3\times 0.04m\times 9.8m/s^2 \\ =-392pa \\ =-392pa\times \frac{1atm}{1.01\times {10}^{5}pa}(1atm=1.01\times {10}^{5}pa) \\ =-3.9\times {10}^{-3}atm \end{gathered}$$

So, the pressure value is$-3.9\times {10}^{-3atm}$

Negative sign indicates that the pressure inside the lung is less than the outside pressure.